x^4 + 4x"' + 7x" + 6x + 2
= x^4 + 4x"' + 3x" + 4x" + 6x + 2
= x"( x" + 4x + 3 ) + 2( 2x" + 3x + 1 )
= x"( x" + x + 3x + 3 ) + 2( 2x" + 2x + x + 1 )
= x"[ x( x + 1 ) + 3( x + 1 ) ] + 2[ 2x( x + 1 ) + ( x + 1 ) ]
= ( x + 1 )[ x"( x + 3 ) + 2( 2x + 1 ) ]
= ( x + 1 )[ x"' + 3x" + 4x + 2 ]
= ( x + 1 )[ x"' + 3x" + 3x + 1 + x + 1 ]
= ( x + 1 )[ ( x + 1 )"' + ( x + 1 ) ]
= ( x + 1 )"[ ( x + 1 )" + 1 ]
= ( x + 1 )"( x" + 2x + 2 )